{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,30]],"date-time":"2026-01-30T22:44:33Z","timestamp":1769813073835,"version":"3.49.0"},"reference-count":7,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2006,10,3]],"date-time":"2006-10-03T00:00:00Z","timestamp":1159833600000},"content-version":"vor","delay-in-days":8525,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1983,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A valuation on a simple graph <jats:italic>G<\/jats:italic> is an assignment of labels to the vertices of <jats:italic>G<\/jats:italic> which induces an assignment of labels to the edges of <jats:italic>G.<\/jats:italic> \u03b2\u2010valuations, also called graceful labelings, and \u03b1\u2010valuations, a subclass of graceful labelings, have an extensive literature; harmonious labelings have been introduced recently by Graham and Sloane. This paper introduces sequential labelings, a subclass of harmonious labelings, and shows that any tree admitting an \u03b1\u2010valuation also admits a sequential labeling and hence is harmonious. Constructions are given for new families of graceful and sequential graphs, generalizing some earlier results. Finally, a conjecture of Frucht is shown to be wrong by exhibiting several graceful labelings of wheels in which the center label is larger than previously thought possible.<\/jats:p>","DOI":"10.1002\/jgt.3190070208","type":"journal-article","created":{"date-parts":[[2007,5,29]],"date-time":"2007-05-29T07:05:50Z","timestamp":1180422350000},"page":"195-201","source":"Crossref","is-referenced-by-count":36,"title":["On sequential labelings of graphs"],"prefix":"10.1002","volume":"7","author":[{"given":"Thom","family":"Grace","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,3]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1749-6632.1979.tb32792.x"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/B978-1-4832-3187-7.50008-8"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1137\/0601045"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.21236\/AD0705364"},{"key":"e_1_2_1_6_2","first-page":"307","article-title":"Graceful cycles","volume":"10","author":"Rao Hebbare S. P.","year":"1976","journal-title":"Utilitas Math."},{"key":"e_1_2_1_7_2","first-page":"261","article-title":"On certain vertex valuations of finite graphs","volume":"4","author":"Kotzig A.","year":"1973","journal-title":"Utilitas Math."},{"key":"e_1_2_1_8_2","first-page":"349","volume-title":"Theory of Graphs (Proc. Int. Symp. Rome, July, 1966)","author":"Rosa A.","year":"1967"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190070208","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190070208","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,26]],"date-time":"2023-09-26T23:28:33Z","timestamp":1695770913000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190070208"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1983,6]]},"references-count":7,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1983,6]]}},"alternative-id":["10.1002\/jgt.3190070208"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190070208","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1983,6]]}}}